12 citations · 20 across the 13 of their papers we have counts for
11 papers · 1 filter
Optimization on Affine-Transversal Hilbert Submanifolds: Part I -- Theoretical Foundations
Yongcun Song, Luhao Xue, Xiaoming Yuan +1
In this paper, we establish the theoretical foundations for the generic optimization problem in a Hilbert space whose feasible set is an affine-transversal Hilbert submanifold give…
Learning to Control: The iUzawa-Net for Nonsmooth Optimal Control of Linear PDEs
Yongcun Song, Xiaoming Yuan, Hangrui Yue +1
We propose an optimization-informed deep neural network approach, named iUzawa-Net, aiming for the first solver that enables real-time solutions for a class of nonsmooth optimal co…
Prox-PINNs: A Deep Learning Algorithmic Framework for Elliptic Variational Inequalities
Yu Gao, Yongcun Song, Zhiyu Tan +2
Elliptic variational inequalities (EVIs) present significant challenges in numerical computation due to their inherent non-smoothness, nonlinearity, and inequality formulations. Tr…
A Single-Loop Stochastic Proximal Quasi-Newton Method for Large-Scale Nonsmooth Convex Optimization
Yongcun Song, Zimeng Wang, Xiaoming Yuan +1
We propose a new stochastic proximal quasi-Newton method for minimizing the sum of two convex functions in the particular context that one of the functions is the average of a larg…
An Operator Learning Approach to Nonsmooth Optimal Control of Nonlinear PDEs
Yongcun Song, Xiaoming Yuan, Hangrui Yue +1
Optimal control problems with nonsmooth objectives and nonlinear partial differential equation (PDE) constraints are challenging, mainly because of the underlying nonsmooth and non…
The Hard-Constraint PINNs for Interface Optimal Control Problems
Ming-Chih Lai, Yongcun Song, Xiaoming Yuan +2
We show that the physics-informed neural networks (PINNs), in combination with some recently developed discontinuity capturing neural networks, can be applied to solve optimal cont…
Accelerated primal-dual methods with enlarged step sizes and operator learning for nonsmooth optimal control problems
Yongcun Song, Xiaoming Yuan, Hangrui Yue
We consider a general class of nonsmooth optimal control problems with partial differential equation (PDE) constraints, which are very challenging due to its nonsmooth objective fu…
The ADMM-PINNs Algorithmic Framework for Nonsmooth PDE-Constrained Optimization: A Deep Learning Approach
Yongcun Song, Xiaoming Yuan, Hangrui Yue
We study the combination of the alternating direction method of multipliers (ADMM) with physics-informed neural networks (PINNs) for a general class of nonsmooth partial differenti…
A numerical approach to the optimal control of thermally convective flows
Yongcun Song, Xiaoming Yuan, Hangrui Yue
The optimal control of thermally convective flows is usually modeled by an optimization problem with constraints of Boussinesq equations that consist of the Navier-Stokes equation…
Bilinear Optimal Control of an Advection-reaction-diffusion System
Roland Glowinski, Yongcun Song, Xiaoming Yuan +1
We consider the bilinear optimal control of an advection-reaction-diffusion system, where the control arises as the velocity field in the advection term. Such a problem is generall…
Implementation of the ADMM to Parabolic Optimal Control Problems with Control Constraints and Beyond
Yongcun Song, Xiaoming Yuan, Hangrui Yue
Parabolic optimal control problems with control constraints are generally challenging, from either theoretical analysis or algorithmic design perspectives. Conceptually, the well-k…